Basic properties
Modulus: | \(6003\) | |
Conductor: | \(2001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(154\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{2001}(500,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6003.cx
\(\chi_{6003}(53,\cdot)\) \(\chi_{6003}(107,\cdot)\) \(\chi_{6003}(152,\cdot)\) \(\chi_{6003}(314,\cdot)\) \(\chi_{6003}(431,\cdot)\) \(\chi_{6003}(458,\cdot)\) \(\chi_{6003}(674,\cdot)\) \(\chi_{6003}(935,\cdot)\) \(\chi_{6003}(953,\cdot)\) \(\chi_{6003}(980,\cdot)\) \(\chi_{6003}(1466,\cdot)\) \(\chi_{6003}(1502,\cdot)\) \(\chi_{6003}(1673,\cdot)\) \(\chi_{6003}(1736,\cdot)\) \(\chi_{6003}(1763,\cdot)\) \(\chi_{6003}(1880,\cdot)\) \(\chi_{6003}(1988,\cdot)\) \(\chi_{6003}(1997,\cdot)\) \(\chi_{6003}(2195,\cdot)\) \(\chi_{6003}(2402,\cdot)\) \(\chi_{6003}(2501,\cdot)\) \(\chi_{6003}(2771,\cdot)\) \(\chi_{6003}(2780,\cdot)\) \(\chi_{6003}(2978,\cdot)\) \(\chi_{6003}(3023,\cdot)\) \(\chi_{6003}(3032,\cdot)\) \(\chi_{6003}(3041,\cdot)\) \(\chi_{6003}(3185,\cdot)\) \(\chi_{6003}(3239,\cdot)\) \(\chi_{6003}(3329,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{77})$ |
Fixed field: | Number field defined by a degree 154 polynomial (not computed) |
Values on generators
\((668,3133,4555)\) → \((-1,e\left(\frac{7}{22}\right),e\left(\frac{3}{7}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 6003 }(2501, a) \) | \(1\) | \(1\) | \(e\left(\frac{87}{154}\right)\) | \(e\left(\frac{10}{77}\right)\) | \(e\left(\frac{19}{77}\right)\) | \(e\left(\frac{29}{154}\right)\) | \(e\left(\frac{107}{154}\right)\) | \(e\left(\frac{125}{154}\right)\) | \(e\left(\frac{6}{77}\right)\) | \(e\left(\frac{13}{77}\right)\) | \(e\left(\frac{58}{77}\right)\) | \(e\left(\frac{20}{77}\right)\) |